13.6 <cfloat>

The <cfloat> header is the C++ version of the C
standard <float.h> header. It defines
parameters that characterize floating-point types in the same way
<climits> does for the integral types. The
native C++ header, <limits>, defines the
same information (and more) using templates instead of macros.

There are three sets of macros, each describing a different
fundamental type. For each type, the corresponding set of macros has
a common prefix: float (FLT_),
double (DBL_), and
longdouble
(LDBL_). Each set characterizes a floating-point
value as a sign, a significand (sometimes called the
mantissa), a base, and an exponent:

x = sign x significand x baseexponent

In everyday arithmetic, we are used to working with a
base of 10. (The base is also called the
radix.) The most common bases for computer
arithmetic, however, are 16 and 2. Many modern workstations use the
IEC 60559 (IEEE 754) standard for floating-point arithmetic, which
uses a base of 2.

The significand is a string of digits in the
given base. There is an implied radix point at the start of the
significand so the value of the significand is always less than 1. (A
radixpoint is the
generalization of a decimal point for any radix.)

A floating-point value is normalized if the
first digit of its significand is nonzero, or if the entire value is
0. A value that is not normalized is
denormalized.

The precision of a floating-point type is the
maximum number of places in the significand. The
range of a floating-point type depends primarily
on the minimum and maximum values for the exponent.

The value returned by each macro is implementation-defined because
all the fundamental types are implementation-defined. The standard
mandates minimum decimal precision and range for each floating-point
type. In this section, the descriptions for the decimal
characteristics of each type include the minimum value set by the
standard.

Only FLT_RADIX expands to a constant expression.
All other macros in <cfloat> expand to
numeric expressions, but the values might not be compile-time
constants.

DBL_DIG macro

Decimal precision

int DBL_DIG

Number of significant decimal digits that can be stored in a
double. The value is always at least 10.

DBL_EPSILON macro

Limit of accuracy

double DBL_EPSILON

The difference between 1 and the smallest value greater than 1 that
can be stored in a double. The value is always
less than or equal to 10-9.

DBL_MANT_DIG macro

Significand precision

int DBL_MANT_DIG

Number of FLT_RADIX digits in the significand of a
double.

DBL_MAX macro

Maximum finite value

double DBL_MAX

Maximum finite double value. The value is always
at least 1037.

DBL_MAX_10_EXP macro

Maximum decimal exponent

int DBL_MAX_10_EXP

Maximum decimal exponent for a finite double. The
value is always at least 37.

DBL_MAX_EXP macro

Maximum exponent

int DBL_MAX_EXP

Maximum exponent of a FLT_RADIX base for a finite
double.

DBL_MIN macro

Minimum positive value

double DBL_MIN

Minimum normalized, positive double value. The
value is always less than or equal to
10-37.

DBL_MIN_10_EXP macro

Minimum decimal exponent

int DBL_MIN_10_EXP

Minimum negative decimal exponent for a normalized
double. The value is always less than or equal to
-37.

DBL_MIN_EXP macro

Minimum exponent

int DBL_MIN_EXP

Minimum negative exponent of a FLT_RADIX base for
a normalized double.

FLT_DIG macro

Decimal precision

int FLT_DIG

Number of significant decimal digits that can be stored in a
float. The value is always at least 6.

FLT_EPSILON macro

Limit of accuracy

float FLT_EPSILON

The difference between 1 and the smallest value greater than 1 that
can be stored in a float. The value is always less
than or equal to 10-5.

FLT_MANT_DIG macro

Significand precision

int FLT_MANT_DIG

Number of FLT_RADIX digits in the significand of a
float.

FLT_MAX macro

Maximum finite value

float FLT_MAX

Maximum finite float value. The value is always at
least 1037.

FLT_MAX_10_EXP macro

Maximum decimal exponent

int FLT_MAX_10_EXP

Maximum decimal exponent for a finite float. The
value is always at least 37.

FLT_MAX_EXP macro

Maximum exponent

int FLT_MAX_EXP

Maximum exponent of a FLT_RADIX base for a finite
float.

FLT_MIN macro

Minimum positive value

float FLT_MIN

Minimum normalized, positive float value. The
value is always less than or equal to
10-37.

FLT_MIN_10_EXP macro

Minimum decimal exponent

int FLT_MIN_10_EXP

Minimum negative decimal exponent for a normalized
float. The value is always less than or equal to
-37.

FLT_MIN_EXP macro

Minimum exponent

int FLT_MIN_EXP

Minimum negative exponent of a FLT_RADIX base for
a normalized float.

FLT_RADIX macro

Implementation base

int FLT_RADIX

The FLT_RADIX macro is an integer constant that
specifies the radix, or base, for the floating-point implementation.
For example, IEC 60559 (IEEE 754) has a FLT_RADIX
of 2.

FLT_ROUNDS macro

Rounding mode

int FLT_ROUNDS

The FLT_ROUNDS macro specifies how the
implementation rounds floating-point numbers. Table 13-2 lists the possible values as defined in the
C++ standard. An implementation can define additional values with
other meanings.

Table 13-2. Floating-point rounding mode

Value

Description

-1

Indeterminable

0

Rounds toward 0

1

Rounds to nearest

2

Rounds up (toward positive infinity)

3

Rounds down (toward negative infinity)

LDBL_DIG macro

Decimal precision

int LDBL_DIG

Number of significant decimal digits that can be stored in a
longdouble.The value is always
at least 10.

LDBL_EPSILON macro

Limit of accuracy

long double LDBL_EPSILON

The difference between 1 and the smallest value greater than 1 that
can be stored in a longdouble.
The value is always less than or equal to
10-9.

LDBL_MANT_DIG macro

Significand precision

int LDBL_MANT_DIG

Number of FLT_RADIX digits in the significand of a
longdouble.

LDBL_MAX macro

Maximum finite value

long double LDBL_MAX

Maximum finite longdouble
value. The value is always at least 1037.

LDBL_MAX_10_EXP macro

Maximum decimal exponent

int LDBL_MAX_10_EXP

Maximum decimal exponent for a finite longdouble. The value is always at least 37.

LDBL_MAX_EXP macro

Maximum exponent

int LDBL_MAX_EXP

Maximum exponent of a FLT_RADIX base for a finite
double.

LDBL_MIN macro

Minimum positive value

long double LDBL_MIN

Minimum normalized, positive longdouble value. The value is always less than or
equal to 10-37.

LDBL_MIN_10_EXP macro

Minimum decimal exponent

int LDBL_MIN_10_EXP

Minimum negative decimal exponent for a normalized
longdouble. The value is
always less than or equal to -37.

LDBL_MIN_EXP macro

Minimum exponent

int LDBL_MIN_EXP

Minimum negative exponent of a FLT_RADIX base for
a normalized longdouble.